L-prime spectrum of a ring

We obtain some new results concerning the fuzzy prime spectrum, such as results about irreducibility and generic points. We show how our results can be applied to the solution of fuzzy intersection equations. We extend the known results to those involving a completely distributive lattice rather than the closed interval [0,1]. In so doing, we open the door to the examination of intersection equations on a lattice rather than the closed interval [0,1].